The components of a position vector of a particle moving in the plane are ))
What is the distance traveled by the particle from t = 1 to t = π?
Answers
Answer:
30.113
Step-by-step explanation:
r(t) = (t³, 2 sin t)
The distance traveled is the length of the path (arc length):
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
L = ∫₁ᵖⁱ √((3t²)² + (2 cos t)²) dt
L = ∫₁ᵖⁱ √(9t⁴ + 4 cos²t) dt
Using a calculator:
L ≈ 30.113
Notice that distance is not the same as displacement. If we wanted to find the displacement:
r(π) = (π³, 0)
r(1) = (1, 2 sin 1)
Δr = √((π³ − 1)² + (0 − 2 sin 1)²)
Δr ≈ 30.053
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I need help with the problem
The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken from population B is 21.2 for a sample of 30. The standard deviation of the sample mean difference is?
Answers
Final answer:
In the scenario, a right triangle is formed with the board, the ground, and the wall. We use the Pythagorean theorem to find the height the board will reach up the wall and get the result as 8 feet.
Explanation:
This is a geometry problem where we need to determine the height the board will reach up the wall. This appears to be a right triangle since the board is leaning against the wall. The length of the board is the hypotenuse (10 feet), and the distance from the wall is one of the legs of the triangle (6 feet).
To find the height the board will reach up the wall, which is the other leg of the triangle, we can use the Pythagorean theorem: a² + b² = c² where a and b are the legs and c is the hypotenuse.
Substitute the given values to the formula: a² + 6² = 10²
Solving this equation gives: a² = 10² - 6²
Then, a² = 64
So, a = √64 = 8
Thus, the height the board will reach up the wall is 8 feet.
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Line
4
has a steeper slope.
Line A
N
Line B
X
-6
4
-2.
2
4
6
-2
4
-6
Answers
Line B has a slope of 4/2
The answer is Line B
Final answer:
The steeper line is determined by comparing the slopes of the two lines. The line with the larger slope value is the steeper line. However, the actual slopes of Line A and Line B in the question are not provided.
Explanation:
From the question, it seems like there are two given lines - Line A and Line B but no specific data is provided about their slopes. Therefore, with the information given, we can't determine which line has the steeper slope. Essentially, the steeper line would be the one with the higher slope value when represented in the form: y = mx + c, where 'm' is the slope. For instance, if Line A had an equation of y = 2x +1 and Line B an equation of y = 4x + 1, Line B's slope is steeper because it has a larger 'm' value compared to Line A.
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Answers
The relative error is plus or minus 4.4 percent .
Answers
The change in Philip's position on the game board is 32 spaces backward.
What is the change in Philip’s position on the game board?
Each card says, "Go back 8 spaces," so for each card drawn, Philip moves back 8 spaces on the game board. Since he drew 4 cards, we can calculate the total change in his position as follows:
Change in position = Number of cards drawn * Spaces moved back for each card
Change in position = 4 * 8
Change in position = 32
So, the change in Philip's position on the game board is 32 spaces backward.
Learn more about word problems at brainly.com/question/20521181
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Answers
Following are the response to the given question:
- When Alina and Cesar are used in the given situation to compare the anticipated journey mileage in mapping software to the actual miles traveled.
- Since Alina's distance will Be less than Cesar's distance, every mile of error results in a greater percentage of errors.
- By using the drop-down menus it completes the assertions about the software's correctness.
- Alina's assessment was 5 miles off now, and Cesar's assessment was 10 miles off, Alina's assessment was 10% off again and Cesar's estimation was 5% off.
Learn more:
Answer:
Because Alina's mileage is LESS than Cesar's mileage, each mile of error results in a GREATER percent error.
Even though Alina's estimate was 5 miles off and Cesar's estimate was 10 miles off, Alina's was 10% off and Cesar's was 5% off.
Step-by-step explanation:
This is right because I got it right on TTM. ;) Trust me, it is.